He et al. (2021) showed that adding a nonionic surfactant at its critical micelle concentration to a pesticide spray suppresses droplet bounce, splash, and powdery-mildew spore ejection on cucumber leaves infected with powdery mildew, and quantified the impact energetics (energy-dissipation fractions, restitution trends, a βmax⁡(We,Re)\beta_{\max}(We,Re) spreading fit) at one fixed surfactant concentration and three pesticide concentrations. Open questions arising from this work include: (i) whether the quantified energetic and dynamical relations generalize across surfactant concentrations, surfactant chemistries, formulations, and droplet-size spectra; (ii) how the mechanisms scale across realistic heterogeneity of the pathogen layer; (iii) the microscopic kinetics of surfactant adsorption and transport at the pathogen-layer interface during the millisecond impact process; and (iv) how field spray volumes and droplet-size spectra should be adjusted to optimize delivered dose while minimizing environmental loss. The quantitative generality of these energetic relations, the dynamic-adsorption mechanism, and the operational optimization of spray volume and droplet-size spectrum remain open.

Background

When a millimetre-sized liquid droplet strikes a solid surface, it spreads, retracts, and may rebound if the surface repels the liquid. Plant leaves are often hydrophobic (water-repelling, with large contact angles) because of their epicuticular wax layer, and some foliar fungal diseases make them more so: powdery mildew is a widespread fungal disease whose mycelium and spores form a loose, porous, hydrophobic white layer on the leaf surface. Pesticide spray droplets impacting such surfaces frequently bounce or splash off, so much of the sprayed dose never reaches the target — a major source of pesticide waste and environmental contamination.

The standard impact-dynamics description uses dimensionless groups built from droplet density ρ\rho, speed UU, diameter DD, viscosity μ\mu, and surface tension σ\sigma: the Weber number We=ρU2D/σWe=\rho U^2 D/\sigma (inertia vs surface tension), the Reynolds number Re=ρUD/μRe=\rho U D/\mu (inertia vs viscosity), and the Ohnesorge number Oh=μ/ρσDOh=\mu/\sqrt{\rho\sigma D} (viscous vs capillary damping). Key observables are the maximum spreading factor βmax⁡\beta_{\max} (largest spread diameter divided by the initial droplet diameter), the restitution coefficient (rebound speed divided by impact speed), and the fraction of impact kinetic energy dissipated during spreading and retraction. A surfactant is a molecule that adsorbs at the air–water interface and lowers surface tension; above the critical micelle concentration (CMC) surfactant monomers additionally aggregate into micelles. Because surfactant must diffuse and adsorb to freshly created interface, the surface tension of a surfactant solution during a millisecond impact is a dynamic quantity (dynamic surface tension), not its equilibrium value — fast-adsorbing surfactants can arrest retraction and pin the contact line before the droplet takes off.

He et al. (2021, ACS Appl. Mater. Interfaces 13, 38018) studied this system experimentally: pesticide (three discrete concentrations) plus a nonionic surfactant at a fixed 0.05% dosage chosen as the CMC, impacting cucumber leaves bearing a powdery-mildew layer. They combined analysis of pinning sites formed during retraction with viscous-dissipation estimates during rebound, quantified energy-dissipation fractions and restitution trends, fitted βmax⁡(We,Re)\beta_{\max}(We,Re), and showed that surfactant addition reduced bounce, splash, and the ejection of mildew spores while increasing adhesion, retention, and (with a trade-off) reducing mass retained per unit area. The same group's companion study (He et al. 2022, ACS Nano 16, 1318) extended the impact-kinematic and pinning-force analysis to mildew layers at different growth stages. Later work by several groups established qualitative structure–function trends — quaternary ammonium surfactants forming semi-micellar structures near the contact line on pear leaves, cationic surfactant chain-length effects on peanut leaves, fatty-alcohol-ethoxylate effects on rust-infected apple leaves, dilution-ratio effects on pathogen-infected wheat leaves — and machine-learning models now screen adjuvants from equilibrium physicochemical properties. A 2025 review of surfactant-enhanced droplet deposition on hydrophobic surfaces (Xiang et al., Adv. Colloid Interface Sci. 336, 103374) nevertheless lists surfactant molecular and convective diffusion during impact and the surfactant–surface interaction among open challenges, and the fundamental rebound-arrest criterion established in 2023 by direct numerical simulation (Ohc+Boc∼1Oh_c+Bo_c\sim 1, with BoBo the Bond number comparing gravity and capillarity) covers only pure, surfactant-free liquids. No study has re-established the source paper's quantified energetic relations as general scaling laws across surfactant chemistries, concentrations, formulations, and droplet-size spectra, characterized the millisecond adsorption kinetics at the pathogen-layer interface, or performed the canopy-scale optimization of spray volume and droplet-size spectrum against delivered dose and environmental loss.

Problem Statement

For surfactant-laden pesticide droplets impacting pathogen-modified hydrophobic leaf surfaces, establish a quantitative, mechanistically grounded, and operationally deployable account of rebound suppression, jointly answering: (1) are the impact-energetic and dynamical relations quantified by He et al. (2021) — energy-dissipation fractions, restitution-coefficient trends, and the maximum-spreading factor βmax⁡(We,Re)\beta_{\max}(We,Re) — general across surfactant concentrations and chemistries, pesticide formulations and particle loads, and droplet-size spectra, and if so in what parameter ranges do they fail or require modification; (2) what are the microscopic mechanisms and kinetics of surfactant adsorption and transport at the porous pathogen-layer interface during the millisecond impact process, including dynamic-surface-tension effects and possible solid–liquid transfer of surfactant into the layer, and how do these produce the observed pinning and dissipation; and (3) given that surfactant addition reduces mass retained per unit area, what adjustments to field spray volumes and droplet-size spectra optimize the trade-off between delivered dose to the target and environmental loss across crop canopies bearing heterogeneous pathogen layers? These three deliverables serve one objective — converting the demonstrated surfactant strategy into a predictive, generalizable, field-deployable deposition technology.

References

  1. He, Lifei; Ding, Lei; Li, Beixing; Mu, Wei; Li, Peiqiang; Liu, Feng. 'Optimization Strategy to Inhibit Droplets Rebound on Pathogen-Modified Hydrophobic Surfaces.' ACS Applied Materials & Interfaces 13(32), 38018–38028, 2021. DOI: 10.1021/acsami.1c07109. https://doi.org/10.1021/acsami.1c07109
  2. He, Lifei; Xi, Shuwen; Ding, Lei; Li, Beixing; Mu, Wei; Li, Peiqiang; Liu, Feng. 'Regulating the Entire Journey of Pesticide Application on Surfaces of Hydrophobic Leaves Modified by Pathogens at Different Growth Stages.' ACS Nano 16(1), 1318–1331, 2022. DOI: 10.1021/acsnano.1c09221. https://doi.org/10.1021/acsnano.1c09221
  3. Song, Yuying; Huang, Qiliang; Liu, Mingxin; Cao, Lidong; Li, Fengmin; Zhao, Pengyue; Cao, Chong. 'Wetting and deposition behaviors of pesticide droplets with different dilution ratios on wheat leaves infected by pathogens.' Journal of Molecular Liquids 370, 120977, 2023. DOI: 10.1016/j.molliq.2022.120977. https://doi.org/10.1016/j.molliq.2022.120977
  4. Kong, Xianhao; Gou, Yueyan; Zhang, Pengjiu; Liu, Zhongfang; Yang, Jing; Fan, Renjun; He, Falin; Gao, Yue; He, Lifei. 'Regulatory role of fatty alcohol ethoxylate surfactants on the bouncing behavior and wetting mechanism of pesticide droplets over rust-infected apple leaves surface.' Colloids and Surfaces A: Physicochemical and Engineering Aspects 728, 138757, 2026. DOI: 10.1016/j.colsurfa.2025.138757. https://doi.org/10.1016/j.colsurfa.2025.138757
  5. He, Lifei; Liu, Xiaolong; Kong, Xianhao; Zhang, Pengjiu; Liu, Zhongfang; Yang, Jing; Fan, Renjun; Gao, Yue. 'Mechanism and strategy of self-assembly of quaternary ammonium surfactant molecules to regulate pesticide droplet impact and wetting of hydrophobic surfaces.' Pest Management Science 81(4), 2040–2050, 2025. DOI: 10.1002/ps.8602. https://doi.org/10.1002/ps.8602
  6. Li, Feng-yu; Yu, Meng; Fang, Yu; Ma, Ying-jian; Wang, Yin-min; Pan, Shou-he; Mu, Lin; Guo, Xin-yu; Pang, Sen; Xu, Yong; Zhao, Rui; Wu, Xue-min. 'Effect of carbon chain length of cationic surfactants on regulating droplet behavior on peanut leaves.' Pest Management Science 81(7), 3505–3515, 2025. DOI: 10.1002/ps.8718. https://doi.org/10.1002/ps.8718
  7. Wu, Yanling; Zhang, Songhao; Bao, Zhenping; Liu, Rui; Sun, Fengzhe; Wang, Yue; Huang, Haiqi; Gao, Yuxia; Ma, Yongqiang; Zhang, Chenhui; Du, Fengpei. 'Bio-based two-dimensional amphiphile with hierarchical self-assembly for enhancing pesticide utilization and reducing environmental risks.' Pest Management Science 81(7), 3493–3504, 2025. DOI: 10.1002/ps.8717. https://doi.org/10.1002/ps.8717
  8. Xiang, Bing; Fang, Kefeng; Song, Runci; Chen, Jie; Feng, Xin; Wang, Guilong; Duan, Xiaoxia; Yang, Chao. 'Advancement in surfactant-enhanced droplet deposition on the hydrophobic surfaces.' Advances in Colloid and Interface Science 336, 103374, 2025. DOI: 10.1016/j.cis.2024.103374. https://doi.org/10.1016/j.cis.2024.103374
  9. Sanjay, Vatsal; Chantelot, Pierre; Lohse, Detlef. 'When does an impacting drop stop bouncing?' Journal of Fluid Mechanics 958, A26, 2023. DOI: 10.1017/jfm.2023.55. https://doi.org/10.1017/jfm.2023.55
  10. Song, Ridan; Wu, Yanling; Bao, Zhenping; Gao, Yuxia; Zhao, Kefei; Zhang, Songhao; Zhang, Chenhui; Du, Fengpei. 'Machine Learning to Predict the Interfacial Behavior of Pesticide Droplets on Hydrophobic Surfaces for Minimizing Environmental Risk.' ACS Sustainable Chemistry & Engineering 10(42), 14034–14044, 2022. DOI: 10.1021/acssuschemeng.2c04779. https://doi.org/10.1021/acssuschemeng.2c04779
  11. Ma, Xiaoxu; Chen, Yanzhen; Song, Yuying; Liu, Mingxin; Cao, Lidong; Zhao, Pengyue; Huang, Qiliang; Cao, Chong. 'Machine learning-based screening of pesticide adjuvants for reduction of pesticide losses on wheat leaf surfaces.' New Plant Protection 1(2), e16, 2024. DOI: 10.1002/npp2.16. https://doi.org/10.1002/npp2.16
  12. Qiao, Baiyu; Liu, Yajia; He, Xiongkui; Wang, Lingxiao; Han, Hu; Zhang, Lanting; Qi, Peng; Liu, Limin; Han, Leng; Xu, Shaoqing; Huang, Zhan; Wu, Tao; Yang, Li. 'Modeling and analysis of droplet deposition behavior: From the micro and macro perspectives.' Computers and Electronics in Agriculture 210, 107896, 2023. DOI: 10.1016/j.compag.2023.107896. https://doi.org/10.1016/j.compag.2023.107896
  13. Wang, Tong; Fan, Ninghui; Cao, Xuesong; Wang, Zhenyu. 'Entire Journey of Foliar Applied Nanomaterials with Different Surfactants Modification on Tomato Leaves and Subsequent Modulation of Stress Resistance.' ACS Nano 20(23), 17029–17044, 2026. DOI: 10.1021/acsnano.6c06235. https://doi.org/10.1021/acsnano.6c06235